1887
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.

Mathematical Modeling Tools to Study Preharvest Food Safety

MyBook is a cheap paperback edition of the original book and will be sold at uniform, low price.
  • PDF
    2.45 MB
  • HTML
    117.50 Kb
  • XML
    101.64 Kb
  • Authors: Cristina Lanzas1, Shi Chen2
  • Editors: Kalmia Kniel3, Siddhartha Thakur4
  • VIEW AFFILIATIONS HIDE AFFILIATIONS
    Affiliations: 1: Department of Population Health and Pathobiology, College of Veterinary Medicine, North Carolina State University, Raleigh, NC 27607; 2: Department of Population Health and Pathobiology, College of Veterinary Medicine, North Carolina State University, Raleigh, NC 27607; 3: Department of Animal and Food Science, University of Delaware, Newark, DE; 4: North Carolina State University, College of Veterinary Medicine, Raleigh, NC
    • Source: microbiolspec August 2016 vol. 4 no. 4 doi:10.1128/microbiolspec.PFS-0001-2013
  • Received 02 February 2015 Accepted 22 April 2015 Published 19 August 2016
  • Cristina Lanzas, [email protected]
image of Mathematical Modeling Tools to Study Preharvest Food Safety
    Preview this microbiology spectrum article:
    Preview Magnify
    Zoom in
    Zoomout

    Mathematical Modeling Tools to Study Preharvest Food Safety, Page 1 of 2

    | /docserver/preview/fulltext/microbiolspec/4/4/PFS-0001-2013-1.gif /docserver/preview/fulltext/microbiolspec/4/4/PFS-0001-2013-2.gif

  • Abstract:

    This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.

  • Citation: Lanzas C, Chen S. 2016. Mathematical Modeling Tools to Study Preharvest Food Safety. Microbiol Spectrum 4(4):PFS-0001-2013. doi:10.1128/microbiolspec.PFS-0001-2013.

References

1. Robinson S. 2004. Simulation. The Practice of Model Development and Use. John Wiley & Sons, West Sussex, England.
2. Otto SP, Day T. 2007. A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Princeton University Press, Princeton, NJ.
3. Lanzas C, Lu Z, Grohn YT. 2011. Mathematical modeling of the transmission dynamics and control of foodborne pathogens and antimicrobial resistance at preharvest. Foodborne Pathog Dis 8:1–10. [PubMed][CrossRef]
4. Keeling MJ, Rohani P. 2008. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton, NJ.
5. Anderson RM, May RM. 1992. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford, England.
6. O’Neill PD. 2010. Introduction and snapshot review: relating infectious disease transmission models to data. Stat Med 29:2069–2077. [PubMed][CrossRef]
7. Sargent RG. 2005. Verification and validation of simulation models. In Kuhl ME, Steiger NM, Armstrong FB, Joines JA (ed), Proc. 2005 Winter Simulation Conference. Orlando, FL. [CrossRef]
8. Sterman JD. 2000. Business Dynamics: System Thinking and Modeling for a Complex World. Irwin McGraw-Hill, Boston, MA.
9. Tedeschi LO. 2006. Assessment of the adequacy of mathematical models. Agric Syst 89:225–247. [CrossRef]
10. Chubb MC, Jacobsen KH. 2010. Mathematical modeling and the epidemiological research process. Eur J Epidemiol 25:13–19. [PubMed][CrossRef]
11. Lipsitch M, Samore MH. 2002. Antimicrobial use and antimicrobial resistance: a population perspective. Emerg Infect Dis 8:347–354. [PubMed][CrossRef]
12. Samore MH, Lipsitch M, Alder SC, Haddadin B, Stoddard G, Williamson J, Sebastian K, Carroll K, Ergonul O, Carmeli Y, Sande MA. 2006. Mechanisms by which antibiotics promote dissemination of resistant pneumococci in human populations. Am J Epidemiol 163:160–170. [PubMed][CrossRef]
13. Saltelli A. 2000. What is sensitivity analysis?, p 3–13. In Saltelli A, Chan K, Scott EM (ed), Sensitivity Analysis. John Wiley & Sons, Ltd, Chichester, England.
14. Lanzas C, Brien S, Ivanek R, Lo Y, Chapagain PP, Ray KA, Ayscue P, Warnick LD, Grohn YT. 2008. The effect of heterogeneous infectious period and contagiousness on the dynamics of Salmonella transmission in dairy cows. Epidemiol Infect 136:1496–1510. [PubMed][CrossRef]
15. Lurette A, Touzeau S, Lamboni M, Monod H. 2009. Sensitivity analysis to identify key parameters influencing Salmonella infection dynamics in a pig batch. J Theor Biol 258:43–52. [PubMed][CrossRef]
16. Lu Z, Grohn YT, Smith RL, Wolfgang DR, Van Kessel JA, Schukken YH. 2009. Assessing the potential impact of Salmonella vaccines in an endemically infected dairy herd. J Theor Biol 259:770–784. [PubMed][CrossRef]
17. Hill AA, Snary EL, Arnold ME, Alban L, Cook AJC. 2008. Dynamics of Salmonella transmission on a British pig grower-finisher farm: a stochastic model. Epidemiol Infect 136:320–333. [PubMed][CrossRef]
18. Katsma WEA, De Koeijer AA, Jacobs-Reitsma WF, Mangen M-JJ, Wagenaar JA. 2007. Assessing interventions to reduce the risk of Campylobacter prevalence in broilers. Risk Anal 27:863–876. [PubMed][CrossRef]
19. Doyle MP, Erickson MC. 2012. Opportunities for mitigating pathogen contamination during on-farm food production. Int J Food Microbiol 152:54–74. [CrossRef]
20. Jordan D, Nielsen LR, Warnick LD. 2008. Modelling a national programme for the control of foodborne pathogens in livestock: the case of Salmonella Dublin in the Danish cattle industry. Epidemiol Inf 136:1521–1536. [PubMed][CrossRef]
21. Doyle MP, Erickson MC. 2006. Reducing the carriage of foodborne pathogens in livestock and poultry. Poultry Sci 85:960–973. [PubMed][CrossRef]
22. Robinson SE, Brown PE, Wright EJ, Hart CA, French NP. 2009. Quantifying within- and between-animal variation and uncertainty associated with counts of Escherichia coli O157 occurring in naturally infected cattle faeces. J R Soc Interface 6:169–177. [PubMed][CrossRef]
23. Lurette A, Belloc C, Touzeau S, Hoch T, Ezanno P, Seegers H, Fourichon C. 2008. Modelling Salmonella spread within a farrow-to-finish pig herd. Vet Res 39:49. [PubMed][CrossRef]
24. van Gerwe T, Miflin JK, Templeton JM, Bouma A, Wagenaar JA, Jacobs-Reitsma WF, Stegeman A, Klinkenberg D. 2009. Quantifying transmission of Campylobacter jejuni in commercial broiler flocks. Appl Environ Microbiol 75:625–628. [PubMed][CrossRef]
25. Zongo P, Viet A-F, Magal P, Beaumont C. 2010. A spatio-temporal model to describe the spread of Salmonella within a laying flock. J Theor Biol 267:595–604. [PubMed][CrossRef]
26. Dougan G, John V, Palmer S, Mastroeni P. 2011. Immunity to salmonellosis. Immunol Rev 240:196–210. [PubMed][CrossRef]
27. McCallum H, Barlow N, Hone J. 2001. How should pathogen transmission be modelled? Trends Ecol Evol 16:295–300. [PubMed][CrossRef]
28. Begon M, Bennett M, Bowers RG, French NP, Hazel SM, Turner J. 2002. A clarification of transmission terms in host-microparasite models: numbers, densities and areas. Epidemiol Infect 129:147–153. [PubMed][CrossRef]
29. Winfield MD, Groisman EA. 2003. Role of nonhost environments in the lifestyles of Salmonella and Escherichia coli. Appl Environ Microbiol 69:3687–3694. [CrossRef]
30. Ayscue P, Lanzas C, Ivanek R, Grohn YT. 2009. Modeling on-farm Escherichia coli O157:H7 population dynamics. Foodborne Path Dis 6:461–470. [PubMed][CrossRef]
31. Gautam R, Bani-Yaghoub M, Neill WH, Döpfer D, Kaspar C, Ivanek R. 2011. Modeling the effect of seasonal variation in ambient temperature on the transmission dynamics of a pathogen with a free-living stage: example of Escherichia coli O157:H7 in a dairy herd. Prev Vet Med 102:10–21. [PubMed][CrossRef]
32. Black DG, Davidson PM. 2008. Use of modeling to enhance the microbiological safety of the food system. Compr Rev Food Sci Food Saf 7:159–167. [CrossRef]
33. Sauli I, Danuser J, Geeraerd AH, Van Impe JF, Rüfenacht J, Bissig-Choisat B, Wenk C, Stärk KDC. 2005. Estimating the probability and level of contamination with Salmonella of feed for finishing pigs produced in Switzerland: the impact of the production pathway. Int J Food Microbiol 100:289–310. [PubMed][CrossRef]
34. Lanzas C, Warnick LD, Ivanek R, Ayscue P, Nydam DV, Grohn YT. 2008. The risk and control of Salmonella outbreaks in calf-raising operations: a mathematical modeling approach. Vet Res 39:61. [PubMed][CrossRef]
35. Lelu M, Langlais M, Poulle ML, Gilot-Fromont E. 2010. Transmission dynamics of Toxoplasma gondii along an urban-rural gradient. Theor Popul Biol 78:139–147. [PubMed][CrossRef]
36. Heffernan JM, Smith RJ, Wahl LM. 2005. Perspectives on the basic reproductive ratio. J R Soc Interface 2:281–293. [PubMed][CrossRef]
37. Laegreid WW, Keen JE. 2004. Estimation of the basic reproduction ratio (R-0) for Shiga toxin-producing Escherichia coli O157 : H7 (STEC O157) in beef calves. Epidemiol Infect 132:291–295. [CrossRef]
38. Chapagain PP, Van Kessel JS, Karns JK, Wolfgang DR, Hovingh E, Nelen KA, Schukken YH, Grohn YT. 2008. A mathematical model of the dynamics of Salmonella cerro infection in a US dairy herd. Epidemiol Infect 136:263–272. [PubMed][CrossRef]
39. Van Schaik G, Klinkenberg D, Veling J, Stegeman A. 2007. Transmission of Salmonella in dairy herds quantified in the endemic situation. Vet Res 38:861–869. [PubMed][CrossRef]
40. Thomas ME, Klinkenberg D, Ejeta G, Van Knapen F, Bergwerff AA, Stegeman JA, Bouma A. 2009. Quantification of horizontal transmission of Salmonella enterica serovar Enteritidis bacteria in pair-housed groups of laying hens. Appl Environ Microbiol 75:6361–6366. [PubMed][CrossRef]
41. Luciani F, Sisson SA, Jiang H, Francis AR, Tanaka MM. 2009. The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis. Proc Natl Acad Sci USA 106:14711–14715. [PubMed][CrossRef]
42. Bäumler AJ, Hargis BM, Tsolis RM. 2000. Tracing the origins of Salmonella outbreaks. Science 287:50–52. [PubMed][CrossRef]
43. Rabsch W, Hargis BM, Tsolis RM, Kingsley RA, Hinz KH, Tschape H, Baumler AJ. 2000. Competitive exclusion of Salmonella enteritidis by Salmonella gallinarum in poultry. Emerg Infect Dis 6:443–448. [PubMed][CrossRef]
44. Levin BR. 2001. Minimizing potential resistance: a population dynamics view. Clin Infect Dis 33:S161–S169. [PubMed][CrossRef]
45. Davis MA, Hancock DD, Besser TE. 2002. Multiresistant clones of Salmonella enterica: The importance of dissemination. J Lab Clin Med 140:135–141. [PubMed][CrossRef]
46. Halloran ME, Longini IM, Jr, Struchiner CJ. 1999. Design and interpretation of vaccine field studies. Epidemiol Rev 21:73–88. [PubMed][CrossRef]
47. Halloran ME, Longini IM, Jr, Struchiner CJ. 2009. Design and Analysis of Vaccine Studies. Springer, New York, NY.
48. Smith DR, Moxley RA, Peterson RE, Klopfenstein TJ, Erickson GE, Bretschneider G, Berberov EM, Clowser S. 2009. A two-dose regimen of a vaccine against type III secreted proteins reduced Escherichia coli O157:H7 colonization of the terminal rectum in beef cattle in commercial feedlots. Foodborne Pathog Dis 6:155–161. [PubMed][CrossRef]
49. Hanski I. 1998. Metapopulation dynamics. Nature 396:41–49. [CrossRef]
50. Liu W-C, Matthews L, Chase-Topping M, Savill NJ, Shaw DJ, Woolhouse MEJ. 2007. Metapopulation dynamics of Escherichia coli O157 in cattle: an exploratory model. J R Soc Interface 4:917–924. [PubMed][CrossRef]
51. Keeling M, Eames K. 2005. Review. Networks and epidemic models. J R Soc Interface 2:295–307. [PubMed][CrossRef]
52. Handcock R, Swain D, Bishop-Hurley G, Patison K, Wark T, Valencia P, Corke P, O’Neill C. 2009. Monitoring animal behaviour and environmental interactions using wireless sensor networks, GPS collars and satellite remote sensing. Sensors 9:3586–3603. [PubMed][CrossRef]
53. Turner J, Bowers RG, Clancy D, Behnke MC, Christley RM. 2008. A network model of E. coli O157 transmission within a typical UK dairy herd: the effect of heterogeneity and clustering on the prevalence of infection. J Theor Biol 254:45–54. [PubMed][CrossRef]
54. Lurette A, Belloc C, Keeling M. 2011. Contact structure and Salmonella control in the network of pig movements in France. Prev Vet Med 102:30–40. [PubMed][CrossRef]
55. Böhm M, Hutchings MR, White PCL. 2009. Contact networks in a wildlife-livestock host community: identifying high-risk individuals in the transmission of bovine TB among badgers and cattle. PLoS One 4:e5016. doi:10.1371/journal.pone.0005016. [PubMed][CrossRef]
56. Burns TE, Guerin MT, Kelton D, Ribble C, Stephen C. 2011. On-farm study of human contact networks to document potential pathways for avian influenza transmission between commercial poultry farms in Ontario, Canada. Transboundary Emerg Dis 58:510–518. [PubMed][CrossRef]
57. McCaig C, Begon M, Norman R, Shankland C. 2011. A symbolic investigation of superspreaders. Bull Math Biol 73:777–794. [PubMed][CrossRef]
58. Grimm V, Revilla E, Berger U, Jeltsch F, Mooij WM, Railsback SF, Thulke H-H, Weiner J, Wiegand T, DeAngelis DL. 2005. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991. [PubMed][CrossRef]
59. Chen S, Sanderson M, Lanzas C. 2013. Investigating effects of between- and within- host variability on Escherichia coli O157 shedding pattern and transmission. Prev Vet Med 109:47–57. [PubMed][CrossRef]
60. Chase-Topping M, Gally D, Low C, Matthews L, Woolhouse M. 2008. Super-shedding and the link between human infection and livestock carriage of Escherichia coli O157. Nat Rev Microbiol 6:904–912. [PubMed][CrossRef]
61. Low JC, McKendrick IJ, McKechnie C, Fenlon D, Naylor SW, Currie C, Smith DGE, Allison L, Gally DL. 2005. Rectal carriage of enterohemorrhagic Escherichia coli O157 in slaughtered cattle. Appl Environ Microbiol 71:93–97. [PubMed][CrossRef]
62. Omisakin F, MacRae M, Ogden ID, Strachan NJC. 2003. Concentration and prevalence of Escherichia coli O157 in cattle feces at slaughter. Appl Environ Microbiol 69:2444–2447. [PubMed][CrossRef]
63. Callaway TR, Edrington TS, Anderson RC, Byrd JA, Nisbet DJ. 2008. Gastrointestinal microbial ecology and the safety of our food supply as related to Salmonella. J Anim Sci 86:E163–E172. [PubMed][CrossRef]
64. Hurley A, Maurer JJ, Lee MD. 2008. Using bacteriophages to modulate Salmonella colonization of the chicken’s gastrointestinal tract: lessons learned from in silico and in vivo modeling. Avian Dis 52:599–607. [PubMed][CrossRef]
65. Wood JC, McKendrick IJ, Gettinby G. 2006. A simulation model for the study of the within-animal infection dynamics of E. coli O157. Prev Vet Med 74:180–193. [PubMed][CrossRef]
66. Wood JC, McKendrick IJ, Gettinby G. 2006. Assessing the efficacy of within-animal control strategies against E. coli O157: a simulation study. Prev Vet Med 74:194–211. [PubMed][CrossRef]
67. Wood JC, Speirs DC, Naylor SW, Gettinby G, McKendrick IJ. 2006. A continuum model of the within-animal population dynamics of E. coli O157. J Biol Syst 14:425–443. [CrossRef]
68. Levin BR, Bull JJ. 2004. Population and evolutionary dynamics of phage therapy. Nat Rev Micro 2:166–173. [PubMed][CrossRef]
69. Andersson DI, Hughes D. 2010. Antibiotic resistance and its cost: is it possible to reverse resistance? Nat Rev Microbiol 8:260–271. [PubMed][CrossRef]
70. Yan SS, Gilbert JM. 2004. Antimicrobial drug delivery in food animals and microbial food safety concerns: an overview of in vitro and in vivo factors potentially affecting the animal gut microflora. Adv Drug Delivery Rev 56:1497–1521. [PubMed][CrossRef]
71. Volkova VV, Lanzas C, Lu Z, Gröhn YT. 2012. Mathematical model of plasmid-mediated resistance to ceftiofur in commensal enteric Escherichia coli of cattle. PLoS One 7:e36738. doi:10.1371/journal.pone.0036738. [PubMed]
72. Ivanek R, Snary EL, Cook AJ, Grohn YT. 2004. A mathematical model for the transmission of Salmonella Typhimurium within a grower-finisher pig herd in Great Britain. J Food Protect 67:2403–2409. [PubMed]
Loading

Article metrics loading...

/content/journal/microbiolspec/10.1128/microbiolspec.PFS-0001-2013
2016-08-19
2020-02-21

Abstract:

This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.

Highlighted Text: Show | Hide
Loading full text...

Full text loading...

/deliver/fulltext/microbiolspec/4/4/PFS-0001-2013.html?itemId=/content/journal/microbiolspec/10.1128/microbiolspec.PFS-0001-2013&mimeType=html&fmt=ahah

Figures

Mathematical Modeling Tools to Study Preharvest Food Safety
[com.pub2web.rdf.cci.facet.ContentItem[id=http://asm.metastore.ingenta.com/content/author/microbiolspec/10.1128/microbiolspec.PFS-0001-2013-1,webId=/content/author/microbiolspec/10.1128/microbiolspec.PFS-0001-2013-1,properties={foaf_givenname=Cristina, foaf_name=Cristina Lanzas, foaf_surname=Lanzas, pub_isAffiliatedWith=[com.pub2web.rdf.cci.facet.ContentItem[id=http://asm.metastore.ingenta.com/content/affiliation/microbiolspec/10.1128/microbiolspec.PFS-0001-2013-aff1]]}], com.pub2web.rdf.cci.facet.ContentItem[id=http://asm.metastore.ingenta.com/content/author/microbiolspec/10.1128/microbiolspec.PFS-0001-2013-2,webId=/content/author/microbiolspec/10.1128/microbiolspec.PFS-0001-2013-2,properties={foaf_givenname=Shi, foaf_name=Shi Chen, foaf_surname=Chen, pub_isAffiliatedWith=[com.pub2web.rdf.cci.facet.ContentItem[id=http://asm.metastore.ingenta.com/content/affiliation/microbiolspec/10.1128/microbiolspec.PFS-0001-2013-aff2]]}]]
Citation: Lanzas C, Chen S. 2016. Mathematical modeling tools to study preharvest food safety. microbiolspec 4(4): doi:10.1128/microbiolspec.PFS-0001-2013
/content/microbiolspec/10.1128/microbiolspec.PFS-0001-2013.fig1
FIGURE 1
The modeling cycle.
microbiolspec/4/4/PFS-0001-2013-fig1_thmb.gif
microbiolspec/4/4/PFS-0001-2013-fig1.gif
Image of FIGURE 1

Click to view

FIGURE 1

The modeling cycle.

Source: microbiolspec August 2016 vol. 4 no. 4 doi:10.1128/microbiolspec.PFS-0001-2013
Permissions and Reprints Request Permissions
Download as Powerpoint
/content/microbiolspec/10.1128/microbiolspec.PFS-0001-2013.fig2
FIGURE 2
Time series (days) of infection prevalence simulated by a stochastic susceptible-infectious model. Ten realizations of the model are presented.
microbiolspec/4/4/PFS-0001-2013-fig2_thmb.gif
microbiolspec/4/4/PFS-0001-2013-fig2.gif
Image of FIGURE 2

Click to view

FIGURE 2

Time series (days) of infection prevalence simulated by a stochastic susceptible-infectious model. Ten realizations of the model are presented.

Source: microbiolspec August 2016 vol. 4 no. 4 doi:10.1128/microbiolspec.PFS-0001-2013
Permissions and Reprints Request Permissions
Download as Powerpoint
/content/microbiolspec/10.1128/microbiolspec.PFS-0001-2013.fig3
FIGURE 3
Examples of flow charts for epidemiological models commonly used for modeling foodborne pathogens in the animal host. –poultry ( 25 ). –dairy cattle ( 14 ). –swine ( 72 ).
microbiolspec/4/4/PFS-0001-2013-fig3_thmb.gif
microbiolspec/4/4/PFS-0001-2013-fig3.gif
Image of FIGURE 3

Click to view

FIGURE 3

Examples of flow charts for epidemiological models commonly used for modeling foodborne pathogens in the animal host. –poultry ( 25 ). –dairy cattle ( 14 ). –swine ( 72 ).

Source: microbiolspec August 2016 vol. 4 no. 4 doi:10.1128/microbiolspec.PFS-0001-2013
Permissions and Reprints Request Permissions
Download as Powerpoint
/content/microbiolspec/10.1128/microbiolspec.PFS-0001-2013.fig4
FIGURE 4
An example of a deterministic compartmental infectious disease model. The flowchart represents an SIRS model. Compartments S, I, and R track the number of individuals who are susceptible, infectious, and recovered, respectively. The triangles represent change in the number of individuals in the compartments. Models that contain both demographic (e.g., births and deaths) and infection flows are called endemic models. Compartmental models are often described mathematically as ordinary differential equations. The ordinary differential equations here describe the inflows and outflows by which the number of individuals in each epidemiological state (S, I, and R) changes over time. The total population, N is equal to S + I + R; υ = birth and death rate; γ = recovery rate of infectious individuals; β = transmission coefficient (transmission is frequency dependent); and = immunity loss rate. The inflow and outflow of a compartment is reflected in the equation. For instance, the S compartment has four arrows associated with it: two inflows and two outflows. The two inflows are birth and loss of immunity from recovered compartment (hence the + sign in the first equation); the two outflows are natural death and infection to infectious compartment (hence the – sign in the first equation). The basic reproduction number of this model.
microbiolspec/4/4/PFS-0001-2013-fig4_thmb.gif
microbiolspec/4/4/PFS-0001-2013-fig4.gif
Image of FIGURE 4

Click to view

FIGURE 4

An example of a deterministic compartmental infectious disease model. The flowchart represents an SIRS model. Compartments S, I, and R track the number of individuals who are susceptible, infectious, and recovered, respectively. The triangles represent change in the number of individuals in the compartments. Models that contain both demographic (e.g., births and deaths) and infection flows are called endemic models. Compartmental models are often described mathematically as ordinary differential equations. The ordinary differential equations here describe the inflows and outflows by which the number of individuals in each epidemiological state (S, I, and R) changes over time. The total population, N is equal to S + I + R; υ = birth and death rate; γ = recovery rate of infectious individuals; β = transmission coefficient (transmission is frequency dependent); and = immunity loss rate. The inflow and outflow of a compartment is reflected in the equation. For instance, the S compartment has four arrows associated with it: two inflows and two outflows. The two inflows are birth and loss of immunity from recovered compartment (hence the + sign in the first equation); the two outflows are natural death and infection to infectious compartment (hence the – sign in the first equation). The basic reproduction number of this model.

Source: microbiolspec August 2016 vol. 4 no. 4 doi:10.1128/microbiolspec.PFS-0001-2013
Permissions and Reprints Request Permissions
Download as Powerpoint
/content/microbiolspec/10.1128/microbiolspec.PFS-0001-2013.fig5
FIGURE 5
Network models are usually represented as graphs. A graph contains a set of nodes (individuals) and edges (contacts) that are associated with these nodes. Shown is an example with five interacting calves. The calves with contact with each other have a line (edge) between them to indicate their mutual relationship . The graph can be translated to an adjacency matrix, which contains as many rows and columns as there are nodes . The elements of the matrix record information about the edges between each pair of nodes, with 1 indicating a contact and 0 meaning no contact.
microbiolspec/4/4/PFS-0001-2013-fig5_thmb.gif
microbiolspec/4/4/PFS-0001-2013-fig5.gif
Image of FIGURE 5

Click to view

FIGURE 5

Network models are usually represented as graphs. A graph contains a set of nodes (individuals) and edges (contacts) that are associated with these nodes. Shown is an example with five interacting calves. The calves with contact with each other have a line (edge) between them to indicate their mutual relationship . The graph can be translated to an adjacency matrix, which contains as many rows and columns as there are nodes . The elements of the matrix record information about the edges between each pair of nodes, with 1 indicating a contact and 0 meaning no contact.

Source: microbiolspec August 2016 vol. 4 no. 4 doi:10.1128/microbiolspec.PFS-0001-2013
Permissions and Reprints Request Permissions
Download as Powerpoint

Supplemental Material

No supplementary material available for this content.

Back to top
This is a required field
Please enter a valid email address
Please check the format of the address you have entered.
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error